Question

Three cooks have to make 80 idlis. They are known to make 20 pieces every minute working together. The first cook began working alone and made 20 pieces having worked for some time more than three minutes. The remaining part of work was done by second and the third cook working together. It took total of 8 minutes to complete the 8 idlis. How many minutes would it take the first cook alone to cook 160 idlis for a marriage party the next day ?

• A. 16 min
• B. 24 min
• C. 32 min
• D. 40 min

Answer 1

The correct option is C 32 min

Let X1 be the number of idlis cooked by first cook per minute
Similarly, X2 and X3
Time required to cok 160 idlis by first cook be T
X1 = 160/T
Time required for 20 idlis = 20 / (160/T) =T/8.........(i)
X2 + X3 = [(80 - 20) / {8 - (T/8)}]
= 480/ (64-T)
X1 + X2 + X3 = 20
(160 / T) + (480 / (64 - T)) = 20
= (8 / T) + (24 / (64 - T)) = 1
64T - T^2 = 612 - 8T + 24T
= 512 - 48T + T^2 = 0
On solving , we get,
T = 16, 32
Given,
T / 8 > 3 ==> T > 24 (Given 8 idlis in more than 3 minutes)
So, T = 32.